N\'eel walls with prescribed winding number and how a nonlocal term can change the energy landscape

TL;DR

This paper investigates how a nonlocal term in a vector field energy model influences the existence and properties of domain wall solutions, revealing new minimizers with specific winding numbers not possible in local models.

Contribution

It demonstrates that nonlocal interactions enable the existence of energy minimizers with prescribed winding numbers, expanding understanding of domain wall configurations in ferromagnetic models.

Findings

Nonlocal term introduces new features in the energy landscape.

Existence of minimizers with prescribed winding numbers.

Nonlocal effects allow configurations forbidden in local models.

Abstract

We study a nonlocal Allen-Cahn type problem for vector fields of unit length, arising from a model for domain walls (called N\'eel walls) in ferromagnetism. We show that the nonlocal term gives rise to new features in the energy landscape; in particular, we prove existence of energy minimisers with prescribed winding number that would be prohibited in a local model.